anonymous
  • anonymous
What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6? f(x) =negative one over six times x squared plus four over three times x plus eleven over six f(x) =one over six times x squared minus four over three times x minus eleven over six f(x) = three fiftieth x squared plus eleven twenty fifth x plus three fifth f(x) = two fiftieth x squared plus eleven twenty fifth x plus two fifth
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@welshfella @nincompoop @Nnesha @ganeshie8
anonymous
  • anonymous
@ASAAD123
Nnesha
  • Nnesha
first we should draw a point at (4,-3) and horizontal line y=-6 |dw:1442578792483:dw| this one is better

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anonymous
  • anonymous
|dw:1442578889393:dw|
Nnesha
  • Nnesha
|dw:1442578826480:dw| yes that's right :=)
Nnesha
  • Nnesha
brb wait a mint plz
Nnesha
  • Nnesha
sorry about alright so now we should pick a point to find distance between the point and focus and distance between the point and directrix you can pick any point |dw:1442579344198:dw|
Nnesha
  • Nnesha
equation would be like this \[\huge\rm \sqrt{(x-a)^2+(y-b)^2} =\sqrt{ (y-c)^2}\] c = directrix (a,b) is a focus point (4,-3) now substitute a ,b c for their values
anonymous
  • anonymous
square root 4-a^2+-3-b=square root-3-c^2
Nnesha
  • Nnesha
well (x,y) is a point that we picked we supposed taht (a,b) is the focus point so replace a with 4 b with -3 and c with -6 c is directix
anonymous
  • anonymous
4-4^2+-3-(-3)=square root-3-(-6)^2 like this?
Nnesha
  • Nnesha
keep the x and y variable \[\large\rm \sqrt{(x-4)^2+(y-(-3))^2} =\sqrt{ (y-(-6))^2}\] like this now take square both sides to cancel out the square root
anonymous
  • anonymous
X^-16+Y+9=Y+36
anonymous
  • anonymous
X^2
anonymous
  • anonymous
is that right
Nnesha
  • Nnesha
hmm no (x-4)^2 = ?
anonymous
  • anonymous
X^2+16
Nnesha
  • Nnesha
hmm no (x-4)^2 is same as (x-4)(x-4) foil it signs are the same in the parentheses so you should get 3 terms
anonymous
  • anonymous
X^2-8x+16
Nnesha
  • Nnesha
yes right \[x^2-8x+16+(y-(-3))^2=(y-(-6))^2\] foil (y-(-3))^2 and then right side
Nnesha
  • Nnesha
here is a hint you will get two terms when you have (a-b)(a+b) opposite signs
anonymous
  • anonymous
Y^2-9
Nnesha
  • Nnesha
hmm no (y-(-3))^2 first distribute -1(-3) ?
anonymous
  • anonymous
thats 3
Nnesha
  • Nnesha
yes so (y+3)^2 is same as (y+3)(y+3)
anonymous
  • anonymous
oh
anonymous
  • anonymous
y^2+6y-9
anonymous
  • anonymous
+9
Nnesha
  • Nnesha
yes right \[\large\rm x^2-8x+16+y^2+6y+9=(y-(-6))^2\] foil right side
anonymous
  • anonymous
Y^2+12y+36
anonymous
  • anonymous
i dont mean to rush but i have to go soon
Nnesha
  • Nnesha
yes right \[\large\rm x^2-8x+16+y^2+6y+9=y^2+12y+36\] foil right side now simplify combine like terms
Nnesha
  • Nnesha
well it will takes some time we need to apply the complete the square method .....
Nnesha
  • Nnesha
\[\large\rm x^2-8x+\color{red}{16}+\color{blue}{y^2}+6y+\color{red}{9}=\color{blue}{y^2}+12y+36\] combine like terms at left side and then move y^2 to the right side let me know what you get
anonymous
  • anonymous
srry but i have to go thank you any ways
Nnesha
  • Nnesha
okay we will finish this whnevr u hve time
princesssleelee
  • princesssleelee
@Nnesha i have this question as well that i need assistance with.

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